《信號(hào)與系統(tǒng)(第二版)》全冊(cè)配套課件

《信號(hào)與系統(tǒng)(第二版)》全冊(cè)配套課件2Signals&Systems3課程說明教學(xué)計(jì)劃學(xué)時(shí):80學(xué)分:5教學(xué)內(nèi)容課堂理論教學(xué)(68學(xué)時(shí))課程設(shè)計(jì)(8學(xué)時(shí))課堂習(xí)題課(4學(xué)時(shí))4課程說明參考書目:《信號(hào)與系統(tǒng)分析》

呂幼新張明友電子工業(yè)出版社

《信號(hào)與系統(tǒng)分析》

閔大鎰朱學(xué)勇電子科技大學(xué)出版社5Chapter1SignalsandSystemsThemathematicaldescriptionandrepresentationsofsignalsandsystems.SignalsandSystemsariseinabroadarrayofapplication.Chapter1SignalsandSystems6Chapter1SignalsandSystems(1)AsimpleRCcircuitSourcevoltageVsandCapacitorvoltageVc(2)Anautomobile7(3)ASpeechSignalChapter1SignalsandSystems8(4)APictureChapter1SignalsandSystems9(5)VerticalWindProfileChapter1SignalsandSystems10信號(hào)的描述頻率特性通信系統(tǒng)中信息:受信者預(yù)先不知道的消息;信號(hào):攜帶消息的物理量;信號(hào)可表示成一個(gè)或多個(gè)自變量的函數(shù);電壓電流系統(tǒng)分析的兩個(gè)共同的基本點(diǎn)：2.系統(tǒng)：對(duì)給定的信號(hào)作出響應(yīng)，并產(chǎn)生新的信號(hào)Chapter1SignalsandSystems1.信號(hào)（一個(gè)或多個(gè)自變量）時(shí)間特性11§1.1Continuous-TimeandDiscrete-TimeSignals

連續(xù)時(shí)間信號(hào)和離散時(shí)間信號(hào)§1.1.1ExamplesandMathematicalRepresentationContinuous-TimeSignals ——Theindependentvariableiscontinuous0t0tChapter1SignalsandSystems12Chapter1SignalsandSystems2.Discrete-TimeSignals ——TheindependentvariableisdiscretenisintegernumberContinuous-timesignalsDiscrete-timesignals§1.1.2SignalEnergyandPower v(t)——voltagei(t)——current13Chapter1SignalsandSystemsi(t)+v(t)-RInstantaneouspower

瞬時(shí)功率Totalenergy14Chapter1SignalsandSystemsTime-averagedpower平均功率①Energysignal②PowersignalEnergysignal0t0tPowersignal0tNeitherenergy,norpower15Chapter1SignalsandSystems§1.2Transformationsoftheindependentvariable§1.2.1Examplesoftransformationsoftheindependentvariable1.Timeshift(時(shí)移)0t1t1Example10otherwisePleaseindicate16Chapter1SignalsandSystems

與波形相同相當(dāng)于左移（超前）to2.Timereversal(時(shí)域反折)0t1t1-t10t1x(-t)isareflectionofx(t)aboutt=0相當(dāng)于右移（延遲）to173.Time-scaling(尺度變換)Chapter1SignalsandSystems0t1t10t1/2t102t1t1a>1信號(hào)壓縮a倍0<a<1信號(hào)擴(kuò)展1/a倍①Continuous-timesignals②Discrete-Timesignalsx[an]n,an∈Nx[n]x[2n]x[n/2]-2024n18Chapter1SignalsandSystemsExample1.1Giventhesignalx(t)→x(-3/2t+1)012t1Solution1-101t1Time-shift-101t1Time-reversal-2/302/3t1Time-scalingSolution2-2-10t1Time-reversal-4/3-2/30t1Time-scaling-2/302/3t1Time-shift19§1.2.2PeriodicsignalsChapter1SignalsandSystemsDiscreten,N——integernumberFundamentalPeriod:min(T,N)(T,N)>0Synthesizethesignal'speriodicT1T2當(dāng)T1/T2為有理數(shù)時(shí)，為周期的ExampleT=2ContinuousT,N≠0——period其中n1,n2互質(zhì)其周期20Chapter1SignalsandSystems§1.2.3EvenandOddSignalsEvenOddEvenOddEvenpartofx(t)

偶部Oddpartofx(t)

奇部012t1-2-1012t1/2-2-1012t1/2-1/221Chapter1SignalsandSystems§1.3ExponentialandSinusoidalSignals

復(fù)指數(shù)信號(hào)和正弦信號(hào)§1.3.1Continuous-TimeComplexExponentialandSinusoidalSignals1.RealExponentialSignalsaisreala>0a<022Chapter1SignalsandSystemsPeriodicComplexExponentialandSinusoidalSignals①PeriodFundamentalPeriod

基本周期ω0FundamentalFrequency23Chapter1SignalsandSystems②Euler’srelation(尤拉關(guān)系)③AveragePower24Chapter1SignalsandSystems④HarmonicrelationBasicSignalCommonPeriodω0FundamentalFrequencykthharmonic25Chapter1SignalsandSystems3.GeneralComplexExponentialSignals26Chapter1SignalsandSystems§1.3.2Discrete-TimeComplexExponentialandSinusoidalSignals

where2.ComplexExponentialSignalsandSinusoidalSignals1.RealExponentialSignalsreal27Chapter1SignalsandSystemsEuler'srelation3.GeneralComplexExponentialSignals28§1.3.3PeriodicityPropertiesofDiscrete-TimeComplexExponentialsChapter1SignalsandSystemsSampling1.2.ω0變化2kπ時(shí)信號(hào)相同29Chapter1SignalsandSystems(a)ω0=0N=1(b)ω0=π/8N=16(c)ω0=π/4N=8(d)ω0=π/2N=4(e)ω0=πN=2低頻高頻(f)ω0=3π/2N=4(g)ω0=7π/4N=8(h)ω0=15π/8N=16(i)ω0=2πN=1Figure1.27ω0=2kπ時(shí),信號(hào)頻率低ω0=(2k+1)π時(shí),信號(hào)頻率高303.PeriodicityPropertiesChapter1SignalsandSystemsRationalNumberFundamentalPeriodisnotperiodic31ω0不同,信號(hào)不同.ω0相差2kπ,信號(hào)相同.ω0越大,頻率越高.ω0=2kπ時(shí),頻率低;ω0=(2k+1)時(shí),頻率高.對(duì)任意的ω0,信號(hào)均為周期的.

為有理數(shù)時(shí),

信號(hào)為周期的.Chapter1SignalsandSystems324.HarmonicallyrelatedperiodicexponentialsChapter1SignalsandSystemsN1=3N2=8N=n1N1=n2N2=24——FundamentalPeriod=133Chapter1SignalsandSystems§1.4TheUnitImpulseandUnitStepFunctions

單位沖激與單位階躍函數(shù)§1.4.1TheDiscrete-TimeUnitImpulseandUnitStepSequencesUnitImpulsen=00n≠0UnitStepn≥00n<0Samplingproperty

取樣特性34Chapter1SignalsandSystems與k無關(guān)Siftingproperty

篩選特性①0求和區(qū)間對(duì)k求和35Chapter1SignalsandSystems求和區(qū)間——FirstDifference（一階差分）BASICSIGNALS時(shí)域分析頻域分析復(fù)頻（Z）域分析36Chapter1SignalsandSystems§1.4.2TheContinuous-TimeUnitStepandUnitImpulseFunctions1.UnitStepFunctiont>00t<00t10△t12.UnitImpulseFunction0t>0?t=00t<0AC+-t=037Chapter1SignalsandSystemsUnitImpulseFunction①0t(1)②0t≠00△t0t-△0△t38Chapter1SignalsandSystems②0t≠039Chapter1SignalsandSystems0t≠t00t0t(1)Ifs(t)iseven,and③0τ積分區(qū)間or,equivalently0τ積分區(qū)間40Chapter1SignalsandSystems§1.4.3ThePropertiesofUnitImpulseFunctions1.SamplingandSiftingproperties①Iff(t)iscontinuousatthepointoft=0②SamplingpropertySiftingproperty41Chapter1SignalsandSystems①設(shè)為在t=0連續(xù)的任意的普通函數(shù)InGeneral0t0t(1)42Chapter1SignalsandSystemsScalingproperty Ifaisreal,a≠0Speciallya=-1——EvenfunctionExample243Chapter1SignalsandSystems§1.4.4信號(hào)的計(jì)算1.信號(hào)的加、減、乘、除Example3442.信號(hào)的基本表示Chapter1SignalsandSystems-τ0τt-τ0t0τt01t1101t0t1-101t1-10t101t2012t145Chapter1SignalsandSystems3.信號(hào)的微分、積分運(yùn)算2101234tExample1.7x(t)isdepictedinFigure1.40(a),determinethederivativeofx(t).-1x(t)01234t(2)(-3)(2)46Chapter1SignalsandSystems§1.5Continuous-timeanddiscrete-timesystemsSystemBeconstitutedbysomeunitsContactwithsomeruleThesystem'sfunctionSystemanalysis（系統(tǒng)分析）Systemsynthesizes（系統(tǒng)綜合）ResearchsystemContinuous-timesystemDiscrete-timesystem47Chapter1SignalsandSystems§1.5.1SimpleExamplesofSystemsLinearConstant-coefficientDifferentialEquationExample1.9LinearConstant-coefficientDifferentialEquationExample1.848Chapter1SignalsandSystemsContinuous-TimeSystemDiscrete-TimeSystemN-orderLinearConstant-coefficientDifferentialEquationN-orderLinearConstant-coefficientDifferenceEquation49Chapter1SignalsandSystems§1.5.2InterconnectionofSystemsSeriesinterconnection(級(jí)聯(lián))Parallelinterconnection(并聯(lián))Feedbackinterconnection(反饋)System1System2inputoutputSystem1System2inputoutputSystem1System2inputoutput50Chapter1SignalsandSystems§1.6BasicSystemProperties§1.6.1SystemswithandwithoutMemory有記憶、無記憶系統(tǒng)無記憶系統(tǒng):

在某時(shí)刻(t)的輸出僅僅與同時(shí)刻(t)的輸入有關(guān)?！猰emoryless（無記憶）——identitysystem,memoryless①②③summer④delay⑤integrateSystemswithmemory51Chapter1SignalsandSystems§1.6.2InvertibilityandInverseSystems可逆系統(tǒng)與可逆性可逆系統(tǒng):

不同的輸入導(dǎo)致不同的輸出（一一對(duì)應(yīng)）。SystemInverseSystem——noninvertiblesystems不可逆系統(tǒng)52Chapter1SignalsandSystems§1.6.3Causality（因果性）因果系統(tǒng):

在某時(shí)刻(t)的輸出只取決于同時(shí)刻(t)或以前(<t)

的輸入。(與該時(shí)刻以后的輸入無關(guān)）③Systemswithoutmemory①②Causalsystems因果系統(tǒng)不可預(yù)測(cè)系統(tǒng)物理上可實(shí)現(xiàn)④53Chapter1SignalsandSystems非因果系統(tǒng):適用于非時(shí)間自變量信號(hào)的處理.NotCausal§1.6.4Stability（穩(wěn)定性）StableSystem①②——notstable——stable54Chapter1SignalsandSystems§1.6.5TimeInvariance（時(shí)不變性）時(shí)不變系統(tǒng):系統(tǒng)參數(shù)不隨時(shí)間改變(恒參系統(tǒng)),系統(tǒng)的輸出波形僅僅取決于輸入波形,而與輸入作用的時(shí)刻無關(guān).IfTimeinvariant時(shí)不變Consideracontinuous-timesystemDelayt0LLDelayt0=timeinvariantsystem≠time-varyingsystem55Chapter1SignalsandSystemsExample1.14Delayt0LLDelayt0EqualTimeinvariantExample1.15NotequalTime-varyingDelayn0LLDelayn056Chapter1SignalsandSystemsExample1.16Delayt0LLDelayt0NotequalTime-varying§1.6.6Linearity（線性）1.InitialState（初始狀態(tài)）輸出取決于輸入的全部歷史57Chapter1SignalsandSystemsInitialState2.Linearity①Additivity②Scaling——Linear58Chapter1SignalsandSystems3.LinearSystemFullresponse①Zero-inputresponseZero-stateresponseInitialstateInput②Zero-inputlinearityWhen59Chapter1SignalsandSystems③Zero-statelinearityIfExample1.17Example1.18It’salinearsystem.It’sanonlinearsystem.It’sanonlinearsystem.Example1.1960Chapter1SignalsandSystemsExample1.20——nonlinearConsiderIncrementallylinear61Chapter1SignalsandSystems線性系統(tǒng)線性系統(tǒng)的三個(gè)特性①微分特性②積分特性頻率保持性： 信號(hào)通過線性系統(tǒng)不會(huì)產(chǎn)生新的頻率分量62Chapter1SignalsandSystems作業(yè)：61.171.21(d)(e)(f)1.22(d)(g)1.231.24(a)(b)1.26(a)(b)1.271.3163Chapter2LinearTime-invariantSystems64Chapter2LTISystemsConsideralineartime-invariantsystemExample1anLTIsystem02t1012t1L024t1-1024t1L65Chapter2LTISystems§2.1Discrete-timeLTISystems:TheConvolutionSum（卷積和）§2.1.1TheRepresentationofDiscrete-TimeSignalsinTermsofimpulsesSiftingProperty離散時(shí)間信號(hào)的沖激表示Example2n66Chapter2LTISystems§2.1.2TheDiscrete-TimeUnitImpulseResponsesandtheConvolution-SumRepresentationofLTISystemsTheUnitImpulseResponses單位沖激響應(yīng)LetLetTime-InvariantUnitImpulseResponses67Chapter2LTISystems2.Convolution-Sum（卷積和）TimeInvariantScalingAdditivityConvolution-Sum（卷積和）系統(tǒng)在n時(shí)刻的輸出包含所有時(shí)刻輸入脈沖的影響k時(shí)刻的脈沖在n時(shí)刻的響應(yīng)68Chapter2LTISystems3.卷積和的計(jì)算①圖解法例2.3圖解法步驟：㈠反折㈡平移㈢求乘積㈣對(duì)每一個(gè)n求和循環(huán)69Chapter2LTISystemsExample2.4DeterminetheoutputsignalSolution(a)n<0(b)0≤n＜4

70Chapter2LTISystems(d)(c)(e)71Chapter2LTISystemsSummarizing,weobtainLy=11Lx=5Lh=7Ly=Lx+Lh-172Chapter2LTISystems不帶進(jìn)位的普通乘法 適用于因果序列或有限長(zhǎng)度序列之間的卷積73Chapter2LTISystemsExample3DetermineSolution3 1 4 2 h[n]2 1 5 x[n]15 5 20 103 1 4 26 2 8 46 5 24 13 22 10y[0]y[1]y[2]y[3]y[4]y[5]y[n]={6,5,24,13, 22,10}n=0,1,2,3,4,574Chapter2LTISystems③多項(xiàng)式算法（適用于有限長(zhǎng)度序列）y[n]={6,5,24,13, 22,10}n=0,1,2,3,4,5利用多項(xiàng)式算法求卷積和的逆運(yùn)算已知y[n]、h[n]→x[n]已知y[n]、x[n]→h[n]75Chapter2LTISystemsExample4Determinex[n]y[n]={6,5,24,13, 22,10}n=0,1,2,3,4,5y(t)076Chapter2LTISystems§2.2Continuous-TimeLTISystems:TheConvolutionIntegral

（卷積積分）§2.2.1TheRepresentationofContinuous-TimeSignalsinTermsofimpulses0△t——SiftingPropertyForexample:77Chapter2LTISystemsAccordingtoSamplingProperty=1§2.2.1TheContinuous-TimeUnitImpulseResponseandthe ConvolutionIntegralRepresentationofLTISystems——TimeInvariant——Scaling78Chapter2LTISystemsConvolutionIntegral卷積積分τ時(shí)刻的沖激t時(shí)刻的響應(yīng)§2.3卷積的計(jì)算一由定義計(jì)算積分例2.6zero-stateoutput79Chapter2LTISystems二圖解法例2.7求下列兩信號(hào)的卷積其余t其余t解：①②③80Chapter2LTISystems④⑤81Chapter2LTISystems§2.3PropertiesofLTISystemsLTI系統(tǒng)的特性可由單位沖激響應(yīng)完全描述Example2.9①LTIsystem——輸入輸出關(guān)系是唯一的82Chapter2LTISystems②NonlinearSystem非線性系統(tǒng)無法用單位沖激響應(yīng)完全描述本課程主要研究線性時(shí)不變（LTI）系統(tǒng)83Chapter2LTISystems§2.3.1PropertiesofConvolutionIntegralandConvolutionSum1.TheCommutativeProperty(交換律）84Chapter2LTISystems2.TheDistributiveProperty(分配律）85Chapter2LTISystems3.TheAssociativeProperty(結(jié)合律）交換積分次序86Chapter2LTISystemsCommutativePropertyAssociativeProperty87Chapter2LTISystems4.含有沖激的卷積①②88Chapter2LTISystems5.卷積的微分、積分性質(zhì)①微分②積分89Chapter2LTISystems③推廣n=1m=-1n>0微分n<0積分90Chapter2LTISystems91Chapter2LTISystemsExampleotherwiseotherwiseSolution10123t0123tIntegral92Chapter2LTISystemsSolution20123t0123t93ExampleConsidertheconvolutionofthetwosignals(1)(1)0t-101t-2-1012t-2-2-1012t-2(-2)94Chapter2LTISystems6幾種典型系統(tǒng)①恒等系統(tǒng)②微分器③積分器④延遲器⑤累加器95Chapter2LTISystems§2.3.4LTISystemswithandwithoutMemory1.Discrete-timeSystemItismemorylessAnLTIsystemwithoutmemory2.Continuous-timeSystemAnLTIsystemwithoutmemory96Chapter2LTISystems§2.3.5InvertibilityofLTISystemsLTI系統(tǒng)的可逆性SystemInverseSystemidentitysystem(恒等系統(tǒng)）97Chapter2LTISystems§2.3.6CausalityforLTISystemsLTI系統(tǒng)的因果性1.Discrete-timeSystem與n時(shí)刻以后輸入有關(guān)Causalsystem2.Continuous-timeSystemCausalsystem98Chapter2LTISystemsConsideralinearsystemCausalInitialRest(初始松弛）Foranytimet0§2.3.7StabilityforLTISystems(穩(wěn)定性）1.Discrete-timeSystem99Chapter2LTISystemsStableSystem2.Continuous-timeSystemabsolutelySummable

絕對(duì)可加StableSystem①Thesystemisstable.②absolutelyIntegrable絕對(duì)可積Thesystemisnotstable.100Chapter2LTISystems§2.3.8TheUnitStepResponseofanLTISystemsLTI系統(tǒng)的單位階躍響應(yīng)Discrete-timeSystemContinuous-timeSystemUnitStepResponseUnitStepResponse101Chapter2LTISystems§2.4SingularityFunctions(奇異函數(shù)）§2.4.1TheUnitImpulseasanIdealizedShortPulse0△t02△t102Chapter2LTISystemsExample2.16Example2.17103DefineChapter2LTISystems§2.4.2DefiningtheUnitImpulsethroughConvolution單位沖激的卷積定義Foranyx(t)Foranynormal,whichiscontinuousattimet=0.Lett=0SiftingPropertyTheunitimpulsehasunitarea104Chapter2LTISystems§2.4.3UnitDoubletsandOtherSingularityFunctions單位沖激偶和其它奇異函數(shù)DerivativeUnitDoublets1.Ingeneral,ktimes0△t0△t105Chapter2LTISystemsDiscrete-timeSystemContinuous-timeSystemCausalsystemCausalsystemStableSystemStableSystem106Chapter2LTISystems3.PropertiesofUnitDoublets（沖激偶的性質(zhì)）2.DefiningForany①②107Chapter2LTISystemsIngeneral,③Derivativesofdifferentordersoftheunitimpulse

單位沖激的各階積分108Chapter2LTISystems§2.5CausalLTISystemsdescribedbyDifferential andDifferenceEquations

用微分方程和差分方程描述的因果LTI系統(tǒng)§2.5.1LinearConstant-coefficientDifferentialEquations

線性常系數(shù)微分方程一經(jīng)典解法1.Homogeneoussolution齊次解特征方程109Chapter2LTISystems①特征方程有N個(gè)不同的單根②特征方程有1個(gè)r階重根，其余N-r個(gè)根各不相同HomogeneousSolution——NaturalResponse

齊次解自然響應(yīng)2.ParticularSolution——ForcedResponse

特解受迫響應(yīng)的函數(shù)形式取決于輸入的函數(shù)形式110Chapter2LTISystems輸入特解C（常數(shù)）B（常數(shù)）

α不是特征單根α是特征單根或111Chapter2LTISystemsExample2.14齊次解：特解：全響應(yīng)：LTI因果系統(tǒng)初始松弛由系統(tǒng)初始條件確定112Chapter2LTISystems②若初始條件不為零，若初始條件不躍變，代入全響應(yīng)N階系統(tǒng)，初始松弛：初始松弛條件下：113Chapter2LTISystems二零輸入、零狀態(tài)解法全響應(yīng)：1.零輸入響應(yīng)：具有齊次解的形式；假定特征方程含有N個(gè)不同的單根2.零狀態(tài)響應(yīng)：齊次解的另一部分特解齊次解的一部分114Chapter2LTISystems由初始狀態(tài)唯一決定零輸入響應(yīng)由零初始狀態(tài)及輸入共同決定零狀態(tài)響應(yīng)由初始狀態(tài)及輸入決定自然響應(yīng)函數(shù)形式由輸入信號(hào)決定受迫響應(yīng)1.零輸入零狀態(tài)解法2.經(jīng)典解法三兩種響應(yīng)分解形式的關(guān)系115Chapter2LTISystemsExample2.14Zero-input responseZero-state response3.Fullresponse116Chapter2LTISystems§2.5.2LinearConstant-coefficientDifferenceEquations

線性常系數(shù)差分方程N(yùn)thorderRecursiveSolution遞推算法RecursiveEquation遞歸方程InputsignalInitialstate117Chapter2LTISystemsParticularlyN=0NonrecursiveEquation非遞歸方程UnitimpulseresponseFiniteimpulseresponse(FIR)systemExample2.15Initialrest118Chapter2LTISystems119Chapter2LTISystems由初始狀態(tài)唯一決定零輸入響應(yīng)由零初始狀態(tài)及輸入共同決定零狀態(tài)響應(yīng)由初始狀態(tài)及輸入決定自然響應(yīng)函數(shù)形式由輸入信號(hào)決定受迫響應(yīng)1.零輸入零狀態(tài)解法2.經(jīng)典解法兩種響應(yīng)分解形式的關(guān)系120Chapter2LTISystems2.差分方程的經(jīng)典解法FullHomogeneousParticular①HomogeneoussolutionEigenequation特征方程(a)特征方程有N個(gè)不同的單根(b)特征方程有1個(gè)r階重根γ1

其余N-r個(gè)根各不相同121Chapter2LTISystems②Particularsolution(ForcedResponse)輸入特解

α不是特征單根α是特征單根或122Chapter2LTISystems3.零輸入、零狀態(tài)解法FullZero-inputZero-state①零輸入響應(yīng)：具有齊次解的形式；②零狀態(tài)響應(yīng)：齊次解的另一部分特解齊次解的一部分假定特征方程含有N個(gè)不同的單根123Chapter2LTISystems由初始狀態(tài)唯一決定零輸入響應(yīng)由零初始狀態(tài)及輸入共同決定零狀態(tài)響應(yīng)由初始狀態(tài)及輸入決定自然響應(yīng)函數(shù)形式由輸入信號(hào)決定受迫響應(yīng)全響應(yīng)零輸入零狀態(tài)解法全響應(yīng)經(jīng)典解法4.兩種響應(yīng)分解形式的關(guān)系124Chapter2LTISystemsExampleConsideranLTIsystem:DeterminethefullresponseSolution1HomogeneousSolutionParticularSolutionFullSolution125Chapter2LTISystemsInitialState:FullSolutionSolution2Zero-inputSolution126Chapter2LTISystemsZero-stateSolut